Question

a garden supply store manager found that if she used a certain function she could determine the price to charge for the shovels to maximize the stores revenue. the graph represents the revenue y of the store if the price per shovel is x dollars. use the graph to find and interpret the symmetry of the function in the context of the situation.

Explanation:

Step1: Identify the axis of symmetry

The graph is a parabola. For a parabola, the axis of symmetry passes through the vertex. Looking at the graph, the vertex (maximum point) occurs at \(x = 40\).

Step2: Interpret the axis of symmetry

The axis of symmetry \(x = 40\) means that the revenue is symmetric about the price of \(40\) dollars per shovel. That is, for any price \(a\) dollars above \(40\), there is a corresponding price \(80 - a\) dollars below \(40\) that gives the same revenue. Also, the maximum revenue occurs when the price per shovel is \(40\) dollars.

Answer:

The axis of symmetry is \(x = 40\). This means that the revenue is symmetric about the price of \(40\) dollars per shovel. The store will earn the maximum revenue when the price per shovel is \(40\) dollars.